I'm realizing now these aren't fantastic pictures, but to try and help, the leaves are dry and brown, just now starting to wilt. Interestingly, the offshoots are still green, however they're starting to turn as well. I'm growing in DC and we just (like everyone) had a very hot heat wave, however everyone got plenty of water an none of the other vines looks this way. They are all first year plants.

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Does this look diseased or just mis-taken care of? I'd like to keep the plant alive, do you trim this down to the ground and start over or just let it fade?

Looks like it might be leaf wilt? As hop vines grow, you should be cutting off all leaves and stems near the ground, ensuring you never remove any more than 25% or so of the vine's overall foliage. As the hop vines grow, keep removing leaves and their stems from the ground up until there are no leaves for the first 4'-5' of the vine's height. Leaf wilt is a ground born disease, similar to tomato blight, that gets splashed up on the leaves and then travels up the vine, killing all the foliage as it goes up. Ensuring there is no foliage near the gorund prevents leaf wilt from taking hold.

It may or may not be leaf wilt, but I don't think it's an insect. Insect damage is rarely seen at a consistent level all over a plant, it tend to be very localized (where the insects are doing their damage) Diseases and fungal infections tend to spread much more rapidly and evenly than insects do.

If it is leaf wilt, I would just cut back all affected leaves from the ground up and go a bit furhter than the diseased leaves, maybe another 12"-18". Leaves that look healthy may have already been infected, so going beyong the point of visible infection should ensure you get all of it.

Upon further inspection this might be a systemic thing. We didn't get any rain here for weeks, it seemed, and in the last 10 days or so we've had several nighttime showers and a couple of big thunderstorms. I'm flying blind with assumptions here but I suspect being wet at night and getting loud rain like that is what sparks the problem.

I've gone and tried to trim the first foot or three; it's something I had been doing but probably too carefully and obviously not with much effect.

Upon further inspection this might be a systemic thing. We didn't get any rain here for weeks, it seemed, and in the last 10 days or so we've had several nighttime showers and a couple of big thunderstorms. I'm flying blind with assumptions here but I suspect being wet at night and getting loud rain like that is what sparks the problem.

I've gone and tried to trim the first foot or three; it's something I had been doing but probably too carefully and obviously not with much effect.

Am I wrong that - judging by the pics - only the one bine is affected by whatever is ailing it? Seems like that would rule out a whole lot of potential issues that would affect the whole lot...

It looks like whatever it is is spreading, which didn't really show true until the last day or two. I went threw Homebrewer's Garden and am trying an epsom salt spray today to address a magnesium deficiency. A bigger fear is some kind of wilt issue, which apparently is a much bigger deal.